A body of mass M attac 8uuds e o ocillates with a period of 4 second. If the mass is increased by 2 kg, the period increases by 1 second. Find the initial mass, assuming that Hooke's law is obeyed.

What will be the period of oscillation (in seconds) of a mass-spring system whose spring has an elastic constant of 110.4 N / m and the mass has a value of 3852.8 g?

An undamped oscillator is driven at its resonance frequency wo by a harmonic force F = F, sin wot. The initial conditions are x, = 0 and vo = 0. (a) Determine r(t). (b) If the breaking strength of the 'spring' of the oscillator is 5F., deduce an equation from which the time t, taken to reach the breaking point can be calculated in terms of wo-

A disk of radius 0.25 meters is attached at its edge to a light (massless) wire of length 0.50 meters to form a physical pendulum.  Assuming small amplitude motion, calculate its period of oscillation.             For a disk, I = (1/2)MR2 about its center of mass.

A-kg mass is attached to a spring with stiffness 25 N/m. The damping constant for the system is 4 N-sec/m. If the 15 55 mass is moved 8 m to the left of equilibrium and given an initial rightward velocity of m/sec, determine the equation of motion of the mass and give its damping factor, quasiperiod, and quasifrequency. What is the equation of motion? y(t) = (Type an exact answer, using radicals as needed.) ***

5 kilogram object is suspended from a string. The string is 4 meters long. What is the period of the object ting as a pendulum? Express your answer a number of seconds, omitting the unit.

A mass-spring-dashpot system is modeled by the differential equation: x" + 4x + 5x = f(t) (a) What is the type of oscillatory motion of the mass? Explain. (b) Find the transient solution of the system. (c) Find the steady state solution of the system for f(t) = 4 cos wt for w= 1. Write your solution as C cos (wt -a). (d) Solve the initial value problem for z(0) = 12, x'(0) = 0. (e) Draw the steady state solution and describe the oscillation.

A boy of mass 45.9 kg standing on the end of a diving board depresses it vertically downward a distance of 18.4 cm. By pushing down on the board with a force a little greater than his weight, the boy can depress the end of the board a bit farther. The boy and the board then oscillate up and down. Estimate the period of oscillation, assuming that the force the board exerts is approximately like that of a compressed spring, in other words, that it obeys Hooke's law.

Hrlp

You cut the tail spring off and meausre the spring force constaant and determine it to be 42.5 N/m. If you apply a 1.35 kg mass to the spring, what will be the period of oscillation?